An analysis of field-dependent water tree growth models

The directly observed growth of individual water trees has been used to examine analytically the applicability of a number of field-dependent growth models. Aqueous electrodes with different radii of curvature have been used to investigate the influence of the inception geometry upon tree growth. Measurements of growth rate have been made over a range of frequencies and the rate constants and compared with the results of dynamic dielectric and mechanical responses, in an attempt to elucidate the material factors that are involved in treeing. It is shown that the frequency dependence of the growth rate cannot be attributed to a modification of the dielectric by the tree, causing a frequency-dependent change of field strength for large enough trees. The rate constants obtained are frequency dependent and the analytical results are consistent with a mechanism of electrical origin, which causes microvoids and crazes to nucleate and grow. In general, the propagation rate of the damage seems to be rate limiting, but in a few cases generally characterized by a sharp inception geometry and thus possibly mechanical strain, it is the nucleation rate that is the slowest